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An ideal filter stops unwanted frequencies and allows others to pass unaltered. The simplest kind of op-amp filter contains one capacitor for each cut-off frequency - i.e. one capacitor for low and high pass, and two for bandpass and bandstop filters. This type is called a first-order filter. The higher the order of the filter, the closer it approaches ideal characteristics, in that the roll-off or attenuation outside the passband is steeper. As a rule of thumb the attenuation outside the passband of a filter in decibels (dB) per octave will be six times the filter order. Thus, a first order filter will have a roll-off of 6dB/octave. If high performance filters are needed the best solution is to use special-purpose filter devices. Filter design is a specialised topic, and although first order filters such as those described here are adequate for many purposes there will inevitably be occasions when something better is needed. Ref. 1 contains further details of filter design.

The non-ideal characteristics of any op-amp mean that bias currents and gain effects must be considered in practical circuits. A DC analysis of bias currents must be undertaken, and the unused input must be earthed through an appropriate resistor as discussed in the appendix.

It must also be remembered that the gain of an op-amp circuit using feedback decreases above a frequency determined by the gain-bandwidth product.

10. LOW-PASS FILTER:

14. THE PRECISION RECTIFIER:

A simple diode will not function as a half-wave rectifier below 0.7V. The circuit of Fig. 4.14(a) provides a solution. When the input is positive the high gain of the op--amp causes the diode to conduct when the noninverting input is only a few microvolts more positive than the inverting input.

Fig. 4.14(a) has two limitations. First, during negative input excursions a large differential voltage is applied to the op-amp, driving it into saturation. An op-amp may take up to 50µseconds to recover from saturation, and this limits high frequency performance. Second, an op-amp which can tolerate large Figure 4.14(b) differential inputs without damage must be used.

Figure 4.14(b)

Figure 14(b) avoids these difficulties. Diode D2 prevents the op-amp becoming saturated, and a faster response is achieved.

15. THE INTEGRATOR:

The circuit is shown in fig. 4.15. The output voltage is found from

The constant is determined by the initial conditions, and can appear as a DC voltage added to the output signal.

An integrator gives a 90š phase shift, since the integral of cosine is sine. This can test the purity of a sinusoid - the signal and its integral form a Lissajous figure on an oscilloscope, and if the gain of the integration is unity, a perfect circle results from a pure sinusoid.

Integrators are also used to generate saw- tooth waveforms, since if a square wave is integrated, a saw-tooth results.

16. THE DIFFERENTIATOR:

Vout = -RC (dVin / dt)

Differentiators (see Figure 4.16) tend to amplify any noise present at the input to the circuit. Noise is usually a "spiky" waveform, and the differential of a spike is likely to be large. Differentiators also suffer from instability problems at high frequencies. Both shortcomings can be overcome to some extent by rolling-off the differentiating action at high frequen-cies. This is achieved by adding RX and CX to the circuit.

17. THE COMPARATOR:

A comparator (see Figure 4.17) is an open-loop op-amp driven into positive or negative saturation according to the difference between the two voltages at its inputs. Since the open loop gain of an op-amp is extremely high the inputs have to be equal within a fraction of a millivolt to avoid saturation. The polarity of the saturated output indicates the direction of the inequality relating the input voltages. Although ordinary op-amps can be used as comparators they take an appreciable time to recover from saturation. Their use as high-speed comparators is also limited by the slew rate. It is better to use special op-amps designed to act as comparators.

N.B. Since there is no feedback, the inputs are not necessarily at the same voltage. Again because there is no feedback, the input impedance is not necessarily constant. As a result the input signal sees a changing load and a changing (small) input current as the comparator output switches. Finally, some comparators will only permit limited differential inputs, as small as 5V in some cases. Check the device datasheet before deciding to use it in a design!

18. CURRENT TO VOLTAGE CONVERTER:

The simplest current to voltage converter is a resistor. However, resistors present a nonzero impedance to the source of input current. This causes difficulties if the current source has very little compliance. (A constant current source can only maintain a constant current through a load over a finite range of load voltage. The output voltage range over which a current source is well behaved is known as its compliance). Figure 4.18 shows how to use an op-amp as a current-to-voltage converter. The inverting input is a virtual earth. The output voltage is determined by the feedback resistor; in the circuit of Fig. 18 it is 1V per µA of input current. The resistor between the noninverting input and ground ensures that the input bias currents match.

19. THE CHARGE AMPLIFIER:

Usually used with capacitive sensors, and for piezoelectric sensors which act as a charge source. A charge amplifier (see Figure 4.19) is only sensitive to variations in charge, meaning that almost any length of connecting cable can be used to connect the sensor and amplifier without affecting the sensitivity.